Combine 3/4 cup buttermilk, oil and vanilla in a glass measuring cup. Make a well in the dry ingredients. Add wet ingredients and stir with a fork until just combined. (Dough will be wet and sticky; do not overmix.)

Spoon dough into 8 mounds on prepared baking sheet. Brush with remaining 2 tablespoons buttermilk and sprinkle with remaining 1/4 cup toasted oats. Bake shortcakes until golden, 10 to 12 minutes. Transfer to a wire rack to cool slightly.
10. To serve, split shortcakes in half with a serrated knife. Set bottoms on dessert plates. Spoon on peach filling and frozen yogurt. Set tops on at an angle. Serve immediately.